Well done on facing it — a payment plan is exactly the right move, and it stops the escalation in its tracks. Here is the timeline as it usually unfolds.
Stage 1 — reminders and penalties. Miss a VAT payment and HMRC sends reminder letters, then a notice of assessment if no return was filed. Penalties and interest start accruing automatically: late-filing penalties, late-payment penalties that escalate the longer the debt is unpaid, and daily interest on the outstanding amount. None of this needs a court — it happens by itself.
Stage 2 — active debt collection. If letters are ignored, the case moves to HMRC's Debt Management unit: firmer letters, phone calls, and possibly a visit from a Field Force officer. They can also set the debt against other amounts HMRC owes you. At this point a Time to Pay arrangement is still usually available — as you have found.
Stage 3 — enforcement. For persistent non-payment HMRC can take control of goods (enforcement agents seize business assets), obtain a county court judgment, apply for a third-party debt order or attachment of earnings, and — for larger debts — petition to wind up the company. Directors should note that ignoring things at this stage can lead to personal liability investigations if the company is insolvent.
Where you are now. A Time to Pay plan pauses enforcement action provided you keep every instalment and stay current on new liabilities — that last part is critical: HMRC will cancel the plan if you fall behind on current VAT returns or payments. Interest generally still accrues during the plan.
The single most important lesson: never ignore HMRC correspondence again. Engaging early — even just to say you cannot pay — almost always produces a better outcome than silence. Keep your plan, file on time, and consider an accountant to keep the returns current.